Add, Subtract, Multiply Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from each polynomial. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + (3x) + (5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms. For example, (3x^2 + 2x) - (x^2 + 4) = (3x^2 - x^2) + (2x) - 4 = 2x^2 + 2x - 4.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

What is the result of adding (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The result is -2x^2 + 11x - 4.

Front

What is the result of multiplying (x - 1) and (x - 8)?

Back

The result is x^2 - 9x + 8.

Front

What is the result of multiplying (3x + 1) and (3x - 1)?

Back

The result is 9x^2 - 1.

Front

What is the result of subtracting (3 - 2x + 2x^2) from (4x - 5 + 3x^2)?

Back

The result is -x^2 - 6x + 8.